Hopfian module

A left (right) module M over a ring R is Hopfian if every surjectiveR-endomorphism of M is an automorphism. Dually, a left (right) R-module M is cohopfian if every injectiveR-endomorphism of M is an automorphism.

References

1 T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York (1999).